A RELOOK AT QUEUEING-INVENTORY SYSTEM WITH RESERVATION, CANCELLATION AND COMMON LIFE TIME

TitleA RELOOK AT QUEUEING-INVENTORY SYSTEM WITH RESERVATION, CANCELLATION AND COMMON LIFE TIME
Publication TypeJournal Article
Year of Publication2016
AuthorsSHAJIN, DHANYA, BENNY, BINITHA, DEEPAK, TG, KRISHNAMOORTHY, A
Secondary TitleCommunications in Applied Analysis
Volume20
Issue4
Start Page545
Pagination30
Date Published11/2016
Type of Workscientific: mathematics
ISSN1083-2564
AMS60J10, 60K25, 90B22
Abstract

In this paper, we study an M/M/1 queue with a storage system having capacity S which have a common life time (CLT), exponentially distributed. On realization of common life time or the first time inventory level drops to zero in a cycle whichever occurs first, a replenishment order is placed so as to bring the inventory level back to S (zero lead time). Customers arrive to the system according to a Poisson process and their service time is exponentially distributed. Reservation of items and cancellation of sold items is permitted before the realization of common life time. Cancellation takes place according to an exponential distribution. In this paper we assume that the time required to cancel the reservation is negligible. When the inventory level becomes zero through service completion or CLT realization, a replenishment order is placed which is realized instantly. We first derive the stationary joint distribution of the queue length and the on-hand inventory in product form. Using the joint distribution, we introduce long-run performance measures and a revenue function. The case of positive lead time is also investigated. Numerical illustrations are provided.
URLhttp://www.acadsol.eu/en/articles/20/4/6.pdf
DOI10.12732/caa.v20i4.6
Short TitleQueueing-Inventory System
Alternate JournalCAA
Refereed DesignationRefereed
Full Text

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